The debate about people's ability to estimate ratios or intervals has raged for decades. This paper describes research that produced the debate, experimental paradigms and research that resolved the debate, and the pitfalls of deriving scales from and basing conclusions on incorrect comparison operations. Historically, researchers believed that respondents followed task instructions when asked to judge ratios or intervals and that resulting numbers represented the scale of sensation for the stimulus dimension. However, nonlinear, nearly exponential relationships consistently resulted from ratio and interval judgments of the same stimuli. This empirical contradiction threatened to defeat the goal of developing single scales of sensation for stimulus dimensions. Recent research employed factorial designs that allow tests of hypothesized comparison models and distinction between subjective and response values. The evidence suggests that people's underlying operation is subtraction when performing both ratios and intervals of two stimuli. Research supports the conclusion that people can compare stimulus information by a ratio operation only when the stimulus information is in the form of differences or distances.